The Most Remarkable Theorem Part I (Theorema Egregium) 

If anyone is wondering the footage from the start of the video is from a movie called “Die Vermessung der Welt”, which is about Gauss and Alexander von Humboldt

I absolutely love this video: content, backdrop, music, etc all of it. Thank you!

Excellent start to a subject that caused many sleepless nights for me 60 years ago... Look forward to the follow-up editions..

Very nicely presented. However, I have to mention that the background music was very loud and distracting which diminished the value of the very good work

Nice intro to the subject of curvature. As you were going along, I thought there would be some discussion of so-called Gaussian, or surface curvature, which for a 2-D manifold embedded in Euclidean 3-space, is specified by a single parameter, but for higher-D manifolds is a tensor (of rank 2? or 4? The Riemann curvature tensor? I'm a little rusty on my differential geometry). But your presentation of linear curvature was spot-on. Anyway, I was hoping the title was referring to the Gauss-Bonet Theorem, a truly remarkable relation between linear and surface curvature! Fred

I love the way you present . Please keep doing more

sweet video! well done and interesting. I love the math vids like numberphine or 3blue1brown etc but i hadnt thought of this before. keep up the great work and cant wait to see what comes next!

I think you'll find that if you apply a similar flow to this form, Shirley's Surface, it will both describe the flow of the universe but also demonstrate a topology for renormalization Why it requires 4pi to complete Surface Surface(cos(u/2)cos(v/2),cos(u/2)sin(v/2), sin(u)/2),u,0,2pi,v,0,4pi

Just as a curve can be defined (whether geometrically, trigonometrically, via calculus, or any other higher math) in terms of a line, a line can in turn be defined in terms of a curve, describing it as the perimeter (or segment of that perimeter) of a circle whose radius is of infinite length

The music is too loud and distracting. Otherwise, good video!

Nice graphics and animations . Very enlightening .

Looking forward to part 2.

Very nice video. Very, very good. It got me back to math video watching in RU-vid. Thanks.

Fantastic video. Thanks!

It still took till 1861 before gleason created a accurate map. A azimuthal equidistant map, as it is, is used today by all Ariel and nautical engineers🎉

Beautiful video ❤

GOAT explanation

1:00 I figured that out as a kid, too, in the context of playing Yahtze. The upper-section bonus needs a certain number of each count, on average. I don't recall the exact chain of reasoning, but I figured out the pattern when trying to rapidly ascess the progress and make decisions on how to fill in the upper section. 1..6 is not as labor-saving as 1.100, but once I realized this, 1..100 was the next thing I did.

9:00 given that there is no "neat" equation to know the perimeter of an ellipse, do we/can we use this ?

This channel finna pop off

yooo let's gooo more differential geometry content!!

This is an amazing video thank you for teaching us about Gaws

great

He prooved it

You can also get that first answer by halving the number you're continuing to, adding .5, then multiplying by the last number again.

This video isn't about spacetime?

Am i the only.one who had never heard of the constructabiloty of the 17 gon..? Or was everyone else new to this also?

Time creates curved surfaces. Though they are same anywhere. Powers create time singularity.

music is a bit intrusive. otherwise, excellent.

Fifty years ago I used the textbook ‘Differential Equations with Applications and Historical Notes’. The historical notes included biographies of relevant mathematicians, and I recall reading there for the first time about Gauss, Euler, LaPlace, Bernoulli etc. Gauss is - arguably - the greatest mathematician of all time. I never liked the story about his adding the first 100 natural numbers. Common sense tells us that this sum is very simple, and there probably isn’t a classroom without at least one student who could not pull off the same trick.

Bros genius is on another level ngl xdd

1:20 What? this is what I thought in my Highschool

Karl Gauss inside doughnut......that was nice

Somewhere out there is a 12-year-old who, after seeing this video, will realize that he wants to be a mathematician.

“Ant Hill high school” 😂

One of the best math videos I've seen, I've noticed I got distracted by the music a lot and had to rewatch some parts...

I am missing the point where derivative is creeped into the formula

This just seems wrong. Imagine if all the internal space of the toroid was filled with really long strings. Would only the strings along the edge wrap around to their end points of would strings in the middle also wrap around to their endpoints. Basically it seems like it should be a sphere or infinite space or a physical barrier along the edge because at the center of the ring on the toroid-let me rephrase this point. If you took a donut with a hole in the middle of it and put in on the table and took a knife and cut it perfectly in half you would see that you now have two circles where the ring crossed through to the other half of the donut. Now in the very center of one of those two circles would space wrap around to itself in a tighter and tigger circle to closer you got to the center of one of the two circles (in the toroidal model of spacetime)? Probably not. What I'm suggesting is that there would be a sorties paradox there to be seen if conceptualize correctly that on one hand you have the edge of the circle which wraps around to itself right? And on the other hand, in the center of the circle you either have just space without any wrapping around onto itself, or a tighter and tighter string that wraps around to its own end getting smaller and smaller the closer you get to the center of the ring of the toroid. It's really hard to explain without being able to point physically at what I'm talking about but it makes more sense that there is a physical wall somewhere out there in the universe or there is just endless space without bounds. Just a thought

It's all pretty obvious if you think about it.

The music is terrible. I downloaded this video so i could watch it undisturbed. I regret it. 7012 different songs, super loud. Can't hear you talk. What were you thinking.

The story attributed here to Gauss, about the sum of integer number is not from Gauss but form Leonard Euler

23:56 🗿

28 × 3 + 63 × 4 = 336

This is called pagadi. Millions of indian🇮🇳 use this🎉🎉🎉

How did Gauss know that he had to divide by 2?

These inventions were already done by several hindu mathematicians way before than european christian mathematicians

You can’t bend a shadow…..nor can you bend space

Please no background music ... Totally distracting and ruines your presentation

This is silly. You can't curve space.

Crap.

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